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Brazil National Olympiad
2006 Brazil National Olympiad
1
1
Part of
2006 Brazil National Olympiad
Problems
(1)
Isosceles triangles
Source: Brazilian Math Olympiad 2006, Problem 1
10/30/2006
Let
A
B
C
ABC
A
BC
be a triangle. The internal bisector of
∠
B
\angle B
∠
B
meets
A
C
AC
A
C
in
P
P
P
and
I
I
I
is the incenter of
A
B
C
ABC
A
BC
. Prove that if
A
P
+
A
B
=
C
B
AP+AB = CB
A
P
+
A
B
=
CB
, then
A
P
I
API
A
P
I
is an isosceles triangle.
geometry
incenter
angle bisector
geometry unsolved